Feedback shift registers are configured to have a linear recurrence equation (LFSR) or nonlinear recurrence equation (NLFSR). Further, feedback shift registers can be configured in the Fibonacci configuration, F(N)LFSR. A further configuration is in the Galois configuration, G(N)LFSR.
In operation of the feedback shift register, a number of register values are fed into a feedback function unit running a feedback function f(D), which is either a linear or nonlinear function of the input register values. Hence, the value of the feedback function f(D) calculated for a current state D yields a feedback value.
In the Fibonacci configuration this feedback value is inserted in the last register Dn-1 in a next clock cycle. In the Galois configuration this feedback value is fed back to additional registers within the chain of registers by means of an Exclusive-Or (XOR) operation, which is an addition in the field F2. In a more general configuration a feedback shift register can have multiple feedback functions whose different feedback values are fed back to different registers in the register chain.
For feedback shift registers in the Galois configuration the feedback function f(D) vanishes. In other words, the value of the register D0 is fed back directly, since the linear recurrence is already fully defined by the selection of the set of feedback position.